From 0d4388b9d71763955768f3ffb7d5d6cb7e7f51e7 Mon Sep 17 00:00:00 2001 From: Justus Kuhlmann Date: Wed, 24 Jul 2024 14:17:53 +0200 Subject: [PATCH] incorporate changes discussed on 23.7. --- talk.tex | 35 ++++++++++++++++++++++------------- 1 file changed, 22 insertions(+), 13 deletions(-) diff --git a/talk.tex b/talk.tex index 0bd3789..ba1c5f6 100644 --- a/talk.tex +++ b/talk.tex @@ -35,7 +35,6 @@ \keywords{Münster} \newcommand{\customcite}[1]{{\color{fu-blue}\citename{#1}{author}}, \citefield{#1}{journaltitle}, {\color{pantone315}\citeyear{#1}}} -\addbibresource{"./My Library.bib"} \begin{document} \begin{frame}[plain] @@ -51,7 +50,13 @@ % differences at sym point? % improvement at the symmetric point % example - +\begin{frame} + \frametitle{What is this all about?} + \begin{itemize} + \item working with exp. Wilson-clover fermions + \item massive $\Rightarrow$ at $N_{\rm f}=3$ symmetric point + \end{itemize} +\end{frame} \begin{frame} \frametitle{Relevance for further improvement and physics} \begin{itemize} @@ -72,13 +77,13 @@ \begin{frame} \frametitle{Determination of $\ca$} \begin{itemize} - \item Schrödinger functional - \item used already \arxivtag{hep-lat/9609035} for $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999} - \item from PCAC mass $m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$ + \item in Schrödinger functional boundary conditions + \item similar in quenched \arxivtag{hep-lat/9609035}, $N_{\rm f} = 2$ \arxivtag{hep-lat/0503003} and std. Wilson-Clover $N_{\rm f} = 3$ \arxivtag{1502.04999} + \item from PCAC mass \end{itemize} \vspace{.5cm} - $$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}$$ - $$\Leftrightarrow \ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$ + $$m_{\rm PCAC} = \frac{\partial_0 f_{\rm A}}{2f_{\rm P}} + \ca \frac{\partial^2_0 f_{\rm P}}{2f_{\rm P}} = r + \ca s$$ + $$m_{\rm PCAC}^{(0)} = m_{\rm PCAC}^{(1)}\quad\Leftrightarrow\quad\ca = - \frac{r^{(1)} - r^{(0)}}{s^{(1)} - s^{(0)}}$$ \end{frame} \begin{frame} @@ -91,6 +96,9 @@ \item also include $\omega_{\rm b4} = {\rm cons.}\;,\quad\omega_{\rm b5} = -r^2~e^{-r/a_0}$ \end{itemize} \item eigenvectors of boundary-to-boundary corr. func. $(F_1)_{i,j} = -\langle O(\omega_{{\rm b}i}) O'(\omega_{{\rm b}j})\rangle$ lead to eigenstates $\pi^{(0)}, \pi^{(1)}$ + \vspace{.5cm} + \pause + \item project $f_{\rm A}$ and $f_{\rm P}$ onto the eigenstates of $F_1$ % Question: do we include all wavefunctions or just some? % How does this interplay with the states that we achieve? % Which is the optimal wf combination? @@ -112,10 +120,10 @@ $L/a$ & $\beta$ & $\kappa_{1}\approx\kappa_{\rm cr}$ & $\kappa_{2}$ & $\kappa_{3}\approx\kappa_{\rm sym}$&$a$\\ \midrule 24&3.685&0.1396980&0.1395500&0.1394400&0.120\\ - 32&3.80&0.1392500&---&0.1389630&\\ - 40&3.90&0.1388562&0.1386148&0.1386030&\\ - 48&4.00&0.1384942&0.1384880&0.1382720&\\ - 56&4.10&0.1381410&0.1380000&0.1379450&\\ + 32&3.80&0.1392500&---&0.1389630&0.095\\ + 40&3.90&0.1388562&0.1386148&0.1386030&0.080\\ + 48&4.00&0.1384942&0.1384880&0.1382720&0.064\\ + 56&4.10&0.1381410&0.1380000&0.1379450&0.055\\ \bottomrule \end{tabular} \end{center} @@ -142,10 +150,11 @@ \framesubtitle{Hit symmetric and critical point exactly} \begin{itemize} \item ensembles not exactly tuned - \item determine points of interest as in \openlat~ensembles + \item able to interpolate to the desired points due to two or three values per $\beta$ + \item determine points of interest as in \openlat~ensembles \arxivtag{2201.03874} \item define: $$\Phi^{\rm SF}_4 = \frac{3}{2}\,8t_0\,|m_{\rm eff}|\,m_{\rm eff} \quad \Rightarrow \quad \Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm cr}}} = 0\,,\;\Phi^{\rm SF}_4\bigm\lvert_{m_{0,{\rm sym}}} = 1.115$$ - \item interpolate to the desired points + \end{itemize} \end{frame}